With this, we consider the relaxation of the discrete feasible set \(\mathcal {X}^M\) , to its convex hull \(\mathcal {P}\) . Note that the set \(\mathcal {P}\)  is a polyhedron and, thus, can described as the solution set of a finite number of linear equalities and inequalities [1]}. Similarly as done in [2]}, [3]} and [4]} the relaxed feasible set is described in real-valued notation using the inequality \(R \left[ x_{\text{r}}^T, 1\right]^T \le 0\) , where \(R= \begin{bmatrix} A, &-b \end{bmatrix}\)  and
\(&\quad A=\begin{bmatrix} (I_M\otimes \beta _1)^T, & (I_M\otimes \beta _2)^T,& \ldots , &(I_M\otimes \beta _{\alpha _x})^T \end{bmatrix}^T \text{,} \\&\quad \beta _i=\begin{bmatrix} \cos {\phi _i},& - \sin {\phi _i}\end{bmatrix} ,\quad \phi _i=\frac{2\pi i }{\alpha _x} \textrm {, for } i=1,\ldots \textrm {,}\ \alpha _x \textrm {,} \quad b=\frac{\cos (\frac{\pi }{\alpha _x})}{\sqrt{{{M}}}} 1_{M\alpha _x} \text{.}\) 
